An axial flow compressor of a gas turbine engine is a multi-stage element that performs work on a fluid, which is typically air, by increasing the pressure of the fluid as it moves through the compressor traveling to a combustion element where the now energized fluid is mixed with a fuel and combusted, and then expanded in a turbine element. The compressor comprises a rotor mounted between at least two bearings and rotates within a compressor casing, which serves as a pressure vessel to contain the energized fluid. The rotor carries a plurality of rotating blades arranged in rows with each rotating blade having an airfoil-shaped cross-section. Interleaved between the rows of rotating blades are rows of stationary blades disposed on the casing wall. Each stage consists of a row of rotating blades followed by a row of stationary blades. As is well known, fluid flow in a multi-stage axial flow compressor is complex by nature because of the proximity of the rotating blades, the buildup of end-wall boundary layers, and the presence of tip leakage flows and secondary flows. All compressors have a limit of stable operation. Beyond this limit the compressor cannot sustain a stable flow pattern, and thus the compressor is not useable.
The compressor is designed for stable operation at a variety of design points, which vary in mass flow and pressure within a design envelope. FIG. 1 illustrates a typical compressor performance map 11, which is a plot of pressure ratio 12 as a function of mass flow 13. Pressure ratio 12 is understood by the skilled artisan to be the ratio of a static or total pressure at the exit of the stage to a total inlet pressure of the stage. When the compressor is operating within the design envelope, the compressor is typically operating along a working line 14, with the working line being comprised of a plurality of design points 16. Design points 16 represent the intersection of the working line 14 with a particular mass flow 13. When the compressor is operating within the design envelope, the air flow through the compressor is essentially uniform and stable around the compressor annulus.
If the compressor is operated too close to a peak pressure rise, disturbances acting on the compressor can cause it to encounter a region where fluid dynamic instabilities, known as rotating stall, develop. On the compressor performance map 11 of FIG. 1, this region of peak pressure rise is illustrate as the region above the working line 14 and bounded by a stall line 18, which is the point where rotating stall will occur for a particular mass flow 13. Additionally, the fluid dynamic instabilities degrade the performance of the compressor and can lead to permanent damage and should be avoided.
Rotating stall results in a localized region of reduced or reversed flow that rotates around the annulus of the flow path and through the compressor. The region is termed as a “stall cell” and typically extends axially through the compressor. Rotating stall results in reduced output from the compressor, can affect only one stage or a group of stages, can lead to a complete fluid flow breakdown through the compressor, and cause a drop in the expected compressor performance or the compressor being loaded in a condition beyond its design. Furthermore, as the stall cell rotates around the annulus of the compressor, it loads and unloads the compressor blades and vanes and can induce fatigue failure.
In many cases, and depending on the operating regime of the compressor, the compressor blades are critically loaded without the capacity, or margin, to absorb the disturbance resulting from the rotating stall. Oftentimes, the stall cells can affect neighboring regions and the stalled region can rapidly grow to become a complete compressor stall that produces catastrophic results to the compressor components. Thus, a compressor must be designed to have a safety margin between the fluid flow and compression ratio at which it will normally be operated and the fluid flow and compression ratio at which a rotating stall will occur. In practical applications, the closer the operating point is to the peak pressure rise, the less the system can tolerate a given disturbance level without entering rotating stall. As a result of the instabilities, compressors are typically operated with the safety margin, or “stall margin.” With continued reference to FIG. 1, the stall margin 19 is a measure of the ratio between peak pressure rise 21, i.e. a pressure rise at stall, and the pressure ratio 22 on the working line 14 of the compressor for a particular flow rate 23. In theory, the greater the stall margin 19, the larger the disturbance the compressor can tolerate before entering rotating stall.
One way of increasing the stall margin for a compressor is through the use of a casing treatment. Generally, the casing treatment modifies the fluid flow at a tip region of the rotating compressor blades by physically altering a wall of the casing. One such alteration is to machine a circumferential air channel or groove in the casing wall proximate the tip region of the rotating blades. With the circumferential grooves applied to the casing wall, the stall cells that prevail when the gas turbine is operating at or near the stall point are encouraged to migrate circumferentially around the casing annulus at the blade tip of the rotating row of blades. Thus, the casing treatment provides a means for the fluid to exit the flow-path where the rotating blade loading is severe and the local pressure ratio high, travel circumferentially around the casing annulus, and re-enter the flow-path at a location where the pressure is more moderate thereby reducing the potential of a tip leakage vortex developing.
At the tip of the rotating compressor blades, a pressure gradient between a pressure side and a suction side of the rotating blade generates a secondary flow that is referred to as tip leakage flow, which is fluid flow passing through a clearance gap between the rotating blade tip and the compressor casing. The tip leakage flow can cause a phenomenon known as a tip leakage vortex to develop, and the behavior of this vortex can promote rotating stall. The tip leakage vortex can extend along the blade to blade passage until it impacts the pressure side of an adjacent blade and disturbs the main flow and affects overall stage performance. With a casing treatment, the tip leakage vortex is essentially sucked into the treated region to reduce a tip region blockage and increase the stall margin. The tip region blockage is caused by a locally high pressure. Thus, a casing wall having circumferential grooves can provide a substantial improvement in the compressor stall margin when compared to a smooth casing wall.
However, an inverse relationship exists between the increase in stall margin that results from application of the casing treatment and the overall compressor efficiency, i.e. improving stall margin via the casing treatment generally causes a reduction in compressor performance. This is largely due to an increase in the tip leakage flow that arises from the casing material being removed by machining the grooves, which increases the flow area above the blade tip. Furthermore, current industrial practices are such that machining a circumferential groove geometry into the casing can be a function of machining capability, rather than aerodynamic and performance considerations. For example, for a given plurality of axially spaced grooves, it can be desirable to have shallow circumferential grooves arranged in the casing above the leading edge of the blade tip. This is because local regions having a high pressure and tip leakage vortices tend to develop toward the trailing edge of the blade tip. Implementing shallow circumferential grooves in the casing near the leading edge of the blade tip would reduce the tip leakage flow when compared to an array of axially spaced grooves machined to the same groove depth. In fact, in some cases, grooves may not be required at all in the casing above the leading edge of the blade. Therefore, tailoring a groove profile or groove geometry for a plurality of axially spaced circumferential grooves to the flow physics at the blade tip can reduce tip leakage losses when compared to traditional approaches, reduce the negative impact of the grooves to compressor performance, and increase stall margin. Accordingly, a need exists for a method of determining a preferred groove geometry for a plurality of axially spaced grooves for a compressor casing treatment to circulate near stagnant air above the blade tip thereby increasing the stall margin of the compressor and offering a greater envelope of reliable operation.